Journal of Convex Analysis 28 (2021), No. 3, [final page numbers not yet available]
Copyright Heldermann Verlag 2021
Convex Bodies with Affinely Equivalent Projections and Affine Bodies of Revolution
IMATE, UNAM, Mexico
We study affine bodies of revolution. This will allow us to prove that a convex body all whose orthogonal n-projections are affinely equivalent is an ellipsoid, provided n ≡ 0, 1, 2 mod 4, n > 1, with the possible exemption of n = 133. Our proof uses convex geometry and topology of compact Lie groups.
Keywords: Affinelly equivalent projections, bodies of revolution, ellipsoids.
MSC: 52A20, 52A21, 22E15.
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